Coulomb Potential in Podolsky-Carroll-Field-Jackiw Electrodynamics

Podolsky electrodynamics, a higher-derivative extension of Maxwell's theory characterized by the Podolsky parameter $\lambda=1/m$, which modifies the photon dispersion relation and regularizes short-distance divergences, is investigated. This framework is then coupled to the Carroll-Field-Jackiw (CFJ) model, in which a Lorentz-violating background four-vector is introduced. Within this extended electrodynamics, the photon propagator is obtained in the combined Podolsky-CFJ framework and subsequently applied to M\"{o}ller scattering. It is shown that the CFJ contribution can reintroduce the short-distance divergence suppressed by Podolsky's term. In the nonrelativistic limit, both the spatial component--which introduces a preferred direction in space and thus breaks isotropy--and the timelike component--which directly affects the dispersion relation--contribute nontrivially to the interaction potential.